30 research outputs found
Functional Equations and the Harmonic Relations for Multiple Zeta Values
Let denote Jacobi's theta function.
We show that the function
satisfies functional equations,
which is a generalization of the harmonic relations
for multiple zeta values
Elliptic Bernoulli Functions And Their Identities
We introduce an elliptic analogue of the Bernoulli functions, which we call elliptic Bernoulli functions. They are defined by using the modified generating function of the elliptic polylogarithms. By degeneration of the elliptic Bernoulli functions, we obtain standard properties and new identities for the Bernoulli functions
Sums of Products of Kronecker's Double Series
Closed expressions are obtained for sums of products of Kronecker's double series.
Corresponding results are derived for
functions which are an elliptic analogue of the periodic Euler polynomials.
As corollaries,
we reproduce the formulas for sums of products of
Bernoulli numbers, Bernoulli polynomials,
Euler numbers, and Euler polynomials,
which were given by K. Dilcher